Numeric Response 4. In an arithmetic series, the first term is -12 and the 15th term is 40. The sum of the first 15 terms is (Record your answer in the numerical-response section below.)

Your answer should be in.0000​

Answers

Answer 1

In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.

If the 15th term is 40, then

40 = -12 + (15 - 1) c   ==>   c = 52/14 = 26/7

We can then write the n-th term as

-12 + (n - 1) 26/7 = (26n - 110)/7

The sum of the first 15 terms is then

[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]

Another way to compute the sum: let S denote the sum,

S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40

Reverse the order of terms:

S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12

Notice that adding up terms in the same position gives the same result,

-12 + 40 = 28

-58/7 + 254/7 = 28

-32/7 + 228/7 = 28

so that

S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28

There are 15 terms in the sum, so

2S = 15×28   ==>   S = 15×28/2 = 210


Related Questions

reduce
0.1 x squared - 8.1 x + 8 = 0 to
2x squared - x + 80 = 0

Answers

Answer:

x = 8

x = -10

Step-by-step explanation:

If the discriminant of an equation is zero, which of the following is true of the equation?​

Answers

[tex]\sf Your \: question \: is \: incomplete. \: [/tex]

______________________

[tex]\sf \: I \: believe \: this \: is \: the \: answer \: you \: wanted[/tex] ⟹

[tex]\sf If \: the \: discriminant \: of \: an \: equation \: is \: zero, \: then \\ \sf \: the \: equation \: will \: have \:\underline{ 1 \: real \: solution \: with \: real \: and \: equal \: roots}.[/tex]

[tex]\boxed{ \sf{Explanation}} [/tex]

[tex]\sf If \: discriminant \: of \: quadratic \: equation \: ax^{2} + bx + c \: \\ \sf is \: b^{2} - 4ac = 0 \: then \: it \: will \: have \\ \sf↦\underline{1 \: real \: solution \: with \: real \: and \: equal \: roots.} [/tex]

Answer:

see explanation

Step-by-step explanation:

If b² - 4ac = 0

Then the roots are real and equal

hello, help needed...again. 35 points !!! please show work for both. thank you:)) due today.

Answers

Answer:

16 direct

17 indirect

Step-by-step explanation:

16.

If it is a direct variation

y/x = constant

4/-2  -2

-8/4 = -2

-12/6 = -2

This is a direct variation

17.

y/x = -1/2 /-2 = 1/4

y/x = -1/-1 = 1

This is not a direct variation

If it is an indirect variation then

yx = constant

-1/2 * -2 = 1

-1*-1 =1

3 * 1/3 =1

This is an indirect variation

Captain Liz is going to load her cruise ship with bags of sugar. She has room for 19 bags of sugar. She has allotted for 121 pounds of sugar on her ship. She can choose from 7-pound bags (the variable s) or 10-pound bags (the variable p). Which equations would be a constraint to Captain Liz maximizing her sugar load?

Correct answers with explanations will earn you brainliest :)

Answers

Answer:

[tex]19 = s + p[/tex] and [tex]121 = 7s + 10p[/tex]

Step-by-step explanation:

First we use constraints given by the problem to set up two equations:

We can only have a total of 19 bags, so:

[tex]19 = s + p[/tex]

Then, we want to maximize her sugar load. Using the info on the weight of each bag and the max carrying capacity:

[tex]121 = 7s + 10p[/tex]

Answer:

Step-by-step explanation:

Let the sugar from 7 pound bags be represented by = s

And let the sugar from 10 pound bags be represented by = p

As given, Captain Liz has room for 19 bags of sugar.

This becomes [tex]s+p=19[/tex]      .......(1)

Also given is , she has room for 19 bags of sugar, so equation becomes:

[tex]7s+10p=121[/tex]     ............(2)

Hence, these are the correct equations.

PLEASE HELP ME! I REALLY NEED HELP

Answers

Answer:

a)

(i) 5.8 hours

(ii)  6.5 hours

(iii) 6 hours

(iv) 6 hours

b) 180 hours

Problem 7:

show that 4^n + 4^n+1 + 4^n+2 + 4^n+3 + 4^n+4 is divisible by 11 for any positive integer

Answers

4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴

= 4ⁿ (4⁰ + 4¹ + 4² + 4³ + 4⁴)

= 4ⁿ × 341

= 4ⁿ × 11 × 31

Someone please help out

Answers

The answer to this question, I believe it is D.

Answer:

Option D

Step-by-step explanation:

Alternate Interior angles are angles that are on the opposite sides of the transversal line (which is the line that cuts across the two parallel lines) and are on the inside of the two parallel lines which in this case is Option D.

△ABCis reflected to form​​ ​△A′B′C′​. The vertices of △ABC are A(3, 1), B(1, 5), and C(6, 9). The vertices of △A′B′C′ are A′(−1, −3), B′(−5, −1), and C′(−9, −6). Which reflection results in the transformation of ​△ABC​​ to ​△A′B′C′​​? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x I NEED HELP PLS The answer choies are: A. Reflection across the x-axis B. Reflection across the y-axis C. Reflection across y = x D. Reflection across y=−x

Answers

Answer:  D) reflection across y = -x

Explanation:

When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).

When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is [tex](x,y) \to (-y,-x)[/tex]

So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).

Similarly, B(1,5) moves to B ' (-5, -1)

Finally, C(6,9) becomes C ' (-9, -6)

How many solutions does it have? Pls help

Answers

Answer:

2 solutions

i hope this will help you

half past 9:00p.m. what is half past of 9:00p.m.​

Answers

Answer:

The answer is 9:30 pm :D.

2. What are the last 2 digits of 1 + 2 + 3 + + 2005 2006​

Answers

Let S be the sum. So you have

S = 1 + 2 + 3 + … + 2004 + 2005 + 2006

as well as

S = 2006 + 2005 + 2004 + … + 3 + 2 + 1

Then

2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)

2S = 2007 + 2007 + … + 2007 + 2007

2S = 2006 × 2007

S = (2006 × 2007)/2

S = 2,013,021

which makes the last two digits 21.


Match each equation with its solution.

Answers

Answer:

1. x = -2 , 3

2. x = - 1, 5

3. -1, 6/5

4. - 0/3, 1.3

Step-by-step explanation:

1.

[tex]ln(x+5)=ln(x-1)+ln(x+1)\\\\x+ 5 = (x-1)(x+1)\\\\x + 5 = x^2 - 1\\\\x^2 - x - 6 = 0 \\\\x^2 - 3 x + 2 x - 6 =0 \\\\x(x-3)+2(x-3)=0\\\\x = -2 and 3[/tex]

2.

[tex]e^{x^{2}}=e^{4x +5}\\\\x^2 - 4x - 5 = 0 \\\\x^2 - 5x + x - 5 = 0 \\\\x (x-5)+1 (x-5)=0\\\\x = -1 and 5[/tex]

3.

[tex]log_{4}(5x^2 +2)=log_{4}(x +8)\\\\5x^2 - x - 6 = 0 \\\\5 x^2 - 6 x + 5x- 6 = 0 \\\\5 x (x + 1)-6(x+1)=0\\\\x = -1 and \frac{6}{5}[/tex]

4.

[tex]log(x-1)+log 5x = 2\\\\5 x (x-1) =2 \\\\5x^2 - 5x -2 = 0 \\\\x = \frac{5\pm\sqrt{25+40}}{10}\\\\x = \frac{5\pm 8}{10}\\\\x = 1.3, - 0.3[/tex]

please help me out really need help

Answers

Answer:

B

add the two together.... 5x^3 is the only cube A or B  only x is 6x and only B  has that

Step-by-step explanation:

Answer:

your answer is B

[tex]f(x)=2x^{2} +6x-4[/tex]

[tex]g(x)=5x^{3} -6x^{2} -3[/tex]

[tex](f+g)x=2x^{2} +6x-4+5x^{3} -6x^{2} -3[/tex]

[tex]=5x^{3} -4x^{2} +6x-7[/tex]

OAmalOHopeO

Please help out with this question..

Answers

Answer:

Step-by-step explanation:

C = 16 * 3 = 48


Find the missing side or angle.
Round to the nearest tenth.
b=3
a=9
c=11
C= ?

Answers

Answer:

C=125°

Step-by-step explanation:

Hi there!

To find angle C, we can use the cosine law:

[tex]cosC=\frac{a^2+b^2-c^2}{2ab}[/tex]

Plug in the given information

[tex]cosC=\frac{9^2+3^2-11^2}{2(9)(3)}[/tex]

[tex]cosC=\frac{-31}{54}[/tex]

[tex]C=cos^-^1(\frac{-31}{54})[/tex]

[tex]C=cos^-^1(\frac{-31}{54})\\C=125[/tex]

Therefore, angle C is approximately 125 degrees.

I hope this helps!

evaluate and solve: y + 3 = –y + 9

Answers

The value of y is 3.

Answer:

Solution given;

: y + 3 = –y + 9

add +y on both term

y+y+3=-y+y+9

subtract both side by 3

2y+3-3=9-3

2y=6

divide both side by 2

2y/2=6/2

y=3

Answer:

y = 3

Step-by-step explanation:

y + 3 = –y + 9

Add y to each side

y+y + 3 = –y +y+ 9

2y +3 = 9

Subtract 3 from each side

2y+3-3 = 9-3

2y = 6

Divide by 2

2y/2 = 6/2

y = 3

A basketball team received a care package and split it evenly among
5 players. If each player received 9 candy bars, how many candy bars
were in the care package?

Help please

Answers

Answer:

45

Step-by-step explanation:

9x5

If m ≠ 1 and mn - 3 = 3 - n , then what is the value of n?
A) 6/ m+1
B) 6/ m-1
C) 6/ m+n
D) 6/ m-n

Answers

[tex]n = \frac{6}{m + 1} [/tex]

Hope it helps you...

The value of n is n= 6/( m+1).

What is expression?

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

mn - 3 = 3 - n

mn + n = 6

n(m+ 1) =6

n= 6/( m+1)

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ2

Express 0.00506 in standard form​

Answers

Answer:

[tex]5.06 x 10^{-3}[/tex]

Step-by-step explanation:

Move decimal 3 place to right.

Because the decimal was moved to right, the exponent is negative.

plsssss helpp in the next 2 min gives 10 points

Answers

Answer:

The answer is 144,5

Step-by-step explanation:

144,5/170×100 =85%

Answer:

200 students in total

Step-by-step explanation:

Mr.Cruz is the director of an after-school program. He says that 170 students, or 85% of the students in his program, went on to attend college. A parent wants to know the total number of students in the program.

?/T = 85%

Where T = Total

85% = 170 students

Set-up the dimensions like this!

part/whole = part/whole

170/T = 85%/100

Multiply 170 by 100

170 • 100 = 17000

Then divided by 85

17000 divided by 85 = 200





order the set of irrational numbers from least to greatest

Answers

Answer:

answer is A

hope it helps please mark as brainliest answer and give me thanks

#Dhruv here

In a triangle ABC, angle BAC = 53° and angle ACB = 28°. If AB is produced to D, find angle CBD.​

Answers

Angle CBD= 81°

I hope it helps you...

Answer:

81

Step-by-step explanation:

∠CBD is the exterior angle of  the ΔABC.

Exterior angle property:

Exterior angle equals the sum of opposite interior angles.

∠CBD = ∠ABC + ∠ACB

           = 53 + 28

           = 81°

y is the element of the set {1.5, 7.2, 3.4, 4.1, 8.9, .75} and 5Y ÷ 6 is an integer. What is the value of Y

Answers

Answer:

7.2

Step-by-step explanation:

5y = 5 *7.2 = 36

36 ÷ 6 = 6

So, y = 7.2

If there were 36 candies and only 12 children, how many candies would each child get?

Answers

Answer:

3 each

Step-by-step explanation:

36 / 12 = 3

.................................................

each would get 3 pieces

Solve the following system of equations by graphing. Label the solution and all intercepts.
4x-2y=8
y=1/2x+2
Please show me also how to graph it. Thanks a ton!

Answers

Answer:

(4,4)

y = 4

x = 4

Step-by-step explanation:

First we need to input y = 1/2x + 2 into 4x - 2y = 8.

4x - 2 (1/2x + 2) = 8 <-- Then solve

4x - 1x + -4 = 8

3x - 4 = 8

    +4   +4

---------------------

3x    =    12

3             3

x = 4

Now we need to use x and apply it to find y.

y = 1/2x + 2

y = 1/2(4) + 2

y = 2 + 2

y = 4

Now to graph go on the x axis (horizontal axis) and go to 4, then up 4 on the y axis.

You need to graph the point (4,4).

I hope this helps!

Answer:

see graph  (4,4)

to manually graph just pick any two values for X in the first equation and calculate the corresponding Y value ... put a "dot" (a point on the graph)

do for both points , and draw al LINE between them...

repeat fore the second equation... the "solution" is where the two lines cross

Step-by-step explanation:

please answer the question below! first to answer correctly, I will mark as brainliest.

Answers

The probability of not winning would be :

1 - probability of winning

This is written as:

1 - n/n+3

Now to simplify as a single fraction rewrite as:

N+3/n+3 - n/n+3

Simplify to get : 3/n+3

Need help ASAp plz and thank you

Answers

Answer:

pls use calculater

Step-by-step explanation:

because i also dont know now what shall i do so its a good suggestion for you i hope

Find square root of 0.0324

Answers

Answer:

0.18

Step-by-step explanation:

Given: F(x) = 2x^2+ 1, G(x) = 2x - 1, H(x) = x
F-2) =

Answers

Answer:

Step-by-step explanation:

A regular hexagon has a radius of 20 in. What is the approximate area of the hexagon?

600 in.2
1,038 in.2
1,200 in.2
2,076 in.2

Answers

Answer:

B

Step-by-step explanation:

A=(3*sqrt(3)*a^2)/2

A=(3*sqrt(3)*400)/2=1038

Answer:

B.  1,038 in.2

Step-by-step explanation:

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